Bc (Bash)

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Surprise surprise: Bash doesn't do floating point arithmatic! There are quite some tools for this, of which bc seems to be the most common. The output of man bc isn't included

Examples

# 1
########################################
#
# * Result: 0
# * Appearantly, you have to specify scale
#
# echo '1/3' | bc


# 2
########################################
#
# Result: .33
#
# echo 'scale=2; 1/3' | bc	


# 3
########################################
#
# i=$(echo 'scale=2; 1/3' | bc)
# echo "i: $i"


# 4 - Doesn't work
########################################
#
# Errors:
#
# (standard_in) 1: illegal character: $
# (standard_in) 1: syntax error
# (standard_in) 1: illegal character: $
#
# Cause: Variables aren't expanded when using single quotes
#
# i1=1
# i2=3
# i3=$(echo 'scale=2; ${i1}/${i2}' | bc)
# #
# echo "i3: $i3"


# 5
########################################
#
# i1=1
# i2=3
# i3=$(echo "scale=2; ${i1}/${i2}" | bc)
# #
# echo "i3: $i3"

See also

Sources

Appendix: man bc

It's quite long, hence not printed at the beginning of the article:

bc(1)                                         General Commands Manual                                         bc(1)

NAME
       bc - An arbitrary precision calculator language

SYNTAX
       bc [ -hlwsqv ] [long-options] [  file ... ]

DESCRIPTION
       bc  is a language that supports arbitrary precision numbers with interactive execution of statements.  There
       are some similarities in the syntax to the C programming language.  A standard math library is available  by
       command  line  option.  If requested, the math library is defined before processing any files.  bc starts by
       processing code from all the files listed on the command line in the order listed.   After  all  files  have
       been  processed, bc reads from the standard input.  All code is executed as it is read.  (If a file contains
       a command to halt the processor, bc will never read from the standard input.)

       This version of bc contains several extensions beyond traditional bc implementations  and  the  POSIX  draft
       standard.  Command line options can cause these extensions to print a warning or to be rejected.  This docu‐
       ment describes the language accepted by this processor.  Extensions will be identified as such.

   OPTIONS
       -h, --help
              Print the usage and exit.

       -i, --interactive
              Force interactive mode.

       -l, --mathlib
              Define the standard math library.

       -w, --warn
              Give warnings for extensions to POSIX bc.

       -s, --standard
              Process exactly the POSIX bc language.

       -q, --quiet
              Do not print the normal GNU bc welcome.

       -v, --version
              Print the version number and copyright and quit.

   NUMBERS
       The most basic element in bc is the number.  Numbers are arbitrary precision  numbers.   This  precision  is
       both in the integer part and the fractional part.  All numbers are represented internally in decimal and all
       computation is done in decimal.  (This version truncates  results  from  divide  and  multiply  operations.)
       There  are  two  attributes of numbers, the length and the scale.  The length is the total number of decimal
       digits used by bc to represent a number and the scale is the total number of decimal digits after the  deci‐
       mal point.  For example:
               .000001 has a length of 6 and scale of 6.
               1935.000 has a length of 7 and a scale of 3.

   VARIABLES
       Numbers  are stored in two types of variables, simple variables and arrays.  Both simple variables and array
       variables are named.  Names begin with a letter followed by any number of letters, digits  and  underscores.
       All  letters  must  be lower case.  (Full alpha-numeric names are an extension.  In POSIX bc all names are a
       single lower case letter.)  The type of variable is clear by the context because all  array  variable  names
       will be followed by brackets ([]).

       There are four special variables, scale, ibase, obase, and last.  scale defines how some operations use dig‐
       its after the decimal point.  The default value of scale is 0.  ibase and obase define the  conversion  base
       for  input  and output numbers.  The default for both input and output is base 10.  last (an extension) is a
       variable that has the value of the last printed number.  These will be discussed in further detail where ap‐
       propriate.  All of these variables may have values assigned to them as well as used in expressions.

   COMMENTS
       Comments in bc start with the characters /* and end with the characters */.  Comments may start anywhere and
       appear as a single space in the input.  (This causes comments to delimit other input items.  For example,  a
       comment can not be found in the middle of a variable name.)  Comments include any newlines (end of line) be‐
       tween the start and the end of the comment.

       To support the use of scripts for bc, a single line comment has been added as an extension.  A  single  line
       comment starts at a # character and continues to the next end of the line.  The end of line character is not
       part of the comment and is processed normally.

   EXPRESSIONS
       The numbers are manipulated by expressions and statements.  Since the language was designed to  be  interac‐
       tive,  statements  and  expressions are executed as soon as possible.  There is no "main" program.  Instead,
       code is executed as it is encountered.  (Functions, discussed in detail  later,  are  defined  when  encoun‐
       tered.)

       A  simple  expression is just a constant. bc converts constants into internal decimal numbers using the cur‐
       rent input base, specified by the variable ibase. (There is an exception in functions.)  The legal values of
       ibase  are  2  through 36. (Bases greater than 16 are an extension.) Assigning a value outside this range to
       ibase will result in a value of 2 or 36.  Input numbers may contain the characters 0–9 and A–Z. (Note:  They
       must  be  capitals.   Lower case letters are variable names.)  Single digit numbers always have the value of
       the digit regardless of the value of ibase. (i.e. A = 10.)  For multi-digit numbers, bc  changes  all  input
       digits greater or equal to ibase to the value of ibase-1.  This makes the number ZZZ always be the largest 3
       digit number of the input base.

       Full expressions are similar to many other high level languages.  Since there is only one  kind  of  number,
       there  are  no rules for mixing types.  Instead, there are rules on the scale of expressions.  Every expres‐
       sion has a scale.  This is derived from the scale of original numbers, the operation performed and  in  many
       cases,  the value of the variable scale. Legal values of the variable scale are 0 to the maximum number rep‐
       resentable by a C integer.

       In the following descriptions of legal expressions, "expr" refers to a complete expression and "var"  refers
       to a simple or an array variable.  A simple variable is just a
              name
       and an array variable is specified as
              name[expr]
       Unless specifically mentioned the scale of the result is the maximum scale of the expressions involved.

       - expr The result is the negation of the expression.

       ++ var The variable is incremented by one and the new value is the result of the expression.

       -- var The variable is decremented by one and the new value is the result of the expression.

       var ++
               The  result  of  the expression is the value of the variable and then the variable is incremented by
              one.

       var -- The result of the expression is the value of the variable and then the  variable  is  decremented  by
              one.

       expr + expr
              The result of the expression is the sum of the two expressions.

       expr - expr
              The result of the expression is the difference of the two expressions.

       expr * expr
              The result of the expression is the product of the two expressions.

       expr / expr
              The  result of the expression is the quotient of the two expressions.  The scale of the result is the
              value of the variable scale.

       expr % expr
              The result of the expression is the "remainder" and it is computed in the following way.  To  compute
              a%b, first a/b is computed to scale digits.  That result is used to compute a-(a/b)*b to the scale of
              the maximum of scale+scale(b) and scale(a).  If scale is set to zero and both expressions  are  inte‐
              gers this expression is the integer remainder function.

       expr ^ expr
              The  result  of the expression is the value of the first raised to the second.  The second expression
              must be an integer.  (If the second expression is not an integer, a warning is generated and the  ex‐
              pression  is truncated to get an integer value.)  The scale of the result is scale if the exponent is
              negative.  If the exponent is positive the scale of the result is the minimum of  the  scale  of  the
              first  expression times the value of the exponent and the maximum of scale and the scale of the first
              expression.  (e.g. scale(a^b) = min(scale(a)*b, max( scale, scale(a))).)  It  should  be  noted  that
              expr^0 will always return the value of 1.

       ( expr )
              This alters the standard precedence to force the evaluation of the expression.

       var = expr
              The variable is assigned the value of the expression.

       var <op>= expr
              This  is equivalent to "var = var <op> expr" with the exception that the "var" part is evaluated only
              once.  This can make a difference if "var" is an array.

       Relational expressions are a special kind of expression that always evaluate to 0 or 1, 0 if the relation is
       false and 1 if the relation is true.  These may appear in any legal expression.  (POSIX bc requires that re‐
       lational expressions are used only in if, while, and for statements and that only one relational test may be
       done in them.)  The relational operators are

       expr1 < expr2
              The result is 1 if expr1 is strictly less than expr2.

       expr1 <= expr2
              The result is 1 if expr1 is less than or equal to expr2.

       expr1 > expr2
              The result is 1 if expr1 is strictly greater than expr2.

       expr1 >= expr2
              The result is 1 if expr1 is greater than or equal to expr2.

       expr1 == expr2
              The result is 1 if expr1 is equal to expr2.

       expr1 != expr2
              The result is 1 if expr1 is not equal to expr2.

       Boolean  operations are also legal.  (POSIX bc does NOT have boolean operations).  The result of all boolean
       operations are 0 and 1 (for false and true) as in relational expressions.  The boolean operators are:

       !expr  The result is 1 if expr is 0.

       expr && expr
              The result is 1 if both expressions are non-zero.

       expr || expr
              The result is 1 if either expression is non-zero.

       The expression precedence is as follows: (lowest to highest)
              || operator, left associative
              && operator, left associative
              ! operator, nonassociative
              Relational operators, left associative
              Assignment operator, right associative
              + and - operators, left associative
              *, / and % operators, left associative
              ^ operator, right associative
              unary - operator, nonassociative
              ++ and -- operators, nonassociative

       This precedence was chosen so that POSIX compliant bc programs will run correctly.  This will cause the  use
       of the relational and logical operators to have some unusual behavior when used with assignment expressions.
       Consider the expression:
              a = 3 < 5

       Most C programmers would assume this would assign the result of "3 < 5" (the value 1) to the  variable  "a".
       What  this  does in bc is assign the value 3 to the variable "a" and then compare 3 to 5.  It is best to use
       parenthesis when using relational and logical operators with the assignment operators.

       There are a few more special expressions that are provided in bc.  These have to do with user defined  func‐
       tions and standard functions.  They all appear as "name(parameters)".  See the section on functions for user
       defined functions.  The standard functions are:

       length ( expression )
              The value of the length function is the number of significant digits in the expression.

       read ( )
              The read function (an extension) will read a number from the standard input, regardless of where  the
              function  occurs.    Beware, this can cause problems with the mixing of data and program in the stan‐
              dard input.  The best use for this function is in a previously written program that needs input  from
              the user, but never allows program code to be input from the user.  The value of the read function is
              the number read from the standard input using the current value of the variable ibase for the conver‐
              sion base.

       scale ( expression )
              The value of the scale function is the number of digits after the decimal point in the expression.

       sqrt ( expression )
              The  value of the sqrt function is the square root of the expression.  If the expression is negative,
              a run time error is generated.

   STATEMENTS
       Statements (as in most algebraic languages) provide the sequencing of expression evaluation.  In  bc  state‐
       ments  are executed "as soon as possible."  Execution happens when a newline in encountered and there is one
       or more complete statements.  Due to this immediate execution, newlines are very important in bc.  In  fact,
       both  a semicolon and a newline are used as statement separators.  An improperly placed newline will cause a
       syntax error.  Because newlines are statement separators, it is possible to hide  a  newline  by  using  the
       backslash character.  The sequence "\<nl>", where <nl> is the newline appears to bc as whitespace instead of
       a newline.  A statement list is a series of statements separated by semicolons and newlines.  The  following
       is  a  list  of  bc statements and what they do: (Things enclosed in brackets ([]) are optional parts of the
       statement.)

       expression
              This statement does one of two things.  If the expression starts with "<variable> <assignment>  ...",
              it  is  considered  to be an assignment statement.  If the expression is not an assignment statement,
              the expression is evaluated and printed to the output.  After the number is  printed,  a  newline  is
              printed.   For example, "a=1" is an assignment statement and "(a=1)" is an expression that has an em‐
              bedded assignment.  All numbers that are printed are printed in the base specified  by  the  variable
              obase.  The legal values for obase are 2 through BC_BASE_MAX.  (See the section LIMITS.)  For bases 2
              through 16, the usual method of writing numbers is used.  For bases greater than 16, bc uses a multi-
              character  digit  method of printing the numbers where each higher base digit is printed as a base 10
              number.  The multi-character digits are separated by spaces.  Each digit contains the number of char‐
              acters  required to represent the base ten value of "obase-1".  Since numbers are of arbitrary preci‐
              sion, some numbers may not be printable on a single output line.  These long numbers  will  be  split
              across lines using the "\" as the last character on a line.  The maximum number of characters printed
              per line is 70.  Due to the interactive nature of bc, printing a number causes the side effect of as‐
              signing  the  printed  value  to the special variable last.  This allows the user to recover the last
              value printed without having to retype the expression that printed the number.  Assigning to last  is
              legal  and  will  overwrite the last printed value with the assigned value.  The newly assigned value
              will remain until the next number is printed or another value is assigned to last.   (Some  installa‐
              tions may allow the use of a single period (.) which is not part of a number as a short hand notation
              for for last.)

       string The string is printed to the output.  Strings start with a double quote  character  and  contain  all
              characters  until  the next double quote character.  All characters are take literally, including any
              newline.  No newline character is printed after the string.

       print list
              The print statement (an extension) provides another method of  output.   The  "list"  is  a  list  of
              strings  and  expressions  separated by commas.  Each string or expression is printed in the order of
              the list.  No terminating newline is printed.  Expressions are evaluated and their value  is  printed
              and  assigned to the variable last.  Strings in the print statement are printed to the output and may
              contain special characters.  Special characters start with the backslash character (\).  The  special
              characters recognized by bc are "a" (alert or bell), "b" (backspace), "f" (form feed), "n" (newline),
              "r" (carriage return), "q" (double quote), "t" (tab), and "\" (backslash).  Any other character  fol‐
              lowing the backslash will be ignored.

       { statement_list }
              This is the compound statement.  It allows multiple statements to be grouped together for execution.

       if ( expression ) statement1 [else statement2]
              The  if  statement  evaluates  the  expression and executes statement1 or statement2 depending on the
              value of the expression.  If the expression is non-zero, statement1 is executed.   If  statement2  is
              present  and  the  value of the expression is 0, then statement2 is executed.  (The else clause is an
              extension.)

       while ( expression ) statement
              The while statement will execute the statement while the expression is non-zero.   It  evaluates  the
              expression  before each execution of the statement.   Termination of the loop is caused by a zero ex‐
              pression value or the execution of a break statement.

       for ( [expression1] ; [expression2] ; [expression3] ) statement
              The for statement controls repeated execution of the statement.  Expression1 is evaluated before  the
              loop.   Expression2  is  evaluated  before  each  execution of the statement.  If it is non-zero, the
              statement is evaluated.  If it is zero, the loop is terminated.  After each execution of  the  state‐
              ment, expression3 is evaluated before the reevaluation of expression2.  If expression1 or expression3
              are missing, nothing is evaluated at the point they would be evaluated.  If expression2  is  missing,
              it  is the same as substituting the value 1 for expression2.  (The optional expressions are an exten‐
              sion.  POSIX bc requires all three expressions.)  The following is equivalent code for the for state‐
              ment:
              expression1;
              while (expression2) {
                 statement;
                 expression3;
              }

       break  This statement causes a forced exit of the most recent enclosing while statement or for statement.

       continue
              The  continue  statement  (an  extension) causes the most recent enclosing for statement to start the
              next iteration.

       halt   The halt statement (an extension) is an executed statement that causes the bc processor to quit  only
              when it is executed.  For example, "if (0 == 1) halt" will not cause bc to terminate because the halt
              is not executed.

       return Return the value 0 from a function.  (See the section on functions.)

       return ( expression )
              Return the value of the expression from a function.  (See the section on functions.)   As  an  exten‐
              sion, the parenthesis are not required.

   PSEUDO STATEMENTS
       These  statements  are  not  statements  in the traditional sense.  They are not executed statements.  Their
       function is performed at "compile" time.

       limits Print the local limits enforced by the local version of bc.  This is an extension.

       quit   When the quit statement is read, the bc processor is terminated, regardless of where the quit  state‐
              ment is found.  For example, "if (0 == 1) quit" will cause bc to terminate.

       warranty
              Print a longer warranty notice.  This is an extension.

   FUNCTIONS
       Functions  provide  a  method  of defining a computation that can be executed later.  Functions in bc always
       compute a value and return it to the caller.  Function definitions are "dynamic" in the sense that  a  func‐
       tion  is  undefined  until a definition is encountered in the input.  That definition is then used until an‐
       other definition function for the same name is encountered.  The new definition then replaces the older def‐
       inition.  A function is defined as follows:
              define name ( parameters ) { newline
                  auto_list   statement_list }
       A function call is just an expression of the form "name(parameters)".

       Parameters  are  numbers  or arrays (an extension).  In the function definition, zero or more parameters are
       defined by listing their names separated by commas.  All parameters are call by  value  parameters.   Arrays
       are  specified  in the parameter definition by the notation "name[]".   In the function call, actual parame‐
       ters are full expressions for number parameters.  The same notation is used for passing arrays as for defin‐
       ing  array  parameters.  The named array is passed by value to the function.  Since function definitions are
       dynamic, parameter numbers and types are checked when a function is called.  Any mismatch in number or types
       of  parameters  will  cause  a  runtime error.  A runtime error will also occur for the call to an undefined
       function.

       The auto_list is an optional list of variables that are for "local" use.  The syntax of the  auto  list  (if
       present)  is  "auto  name, ... ;".  (The semicolon is optional.)  Each name is the name of an auto variable.
       Arrays may be specified by using the same notation as used in parameters.  These variables have their values
       pushed  onto  a  stack  at  the  start of the function.  The variables are then initialized to zero and used
       throughout the execution of the function.  At function exit, these variables are popped so that the original
       value  (at  the  time of the function call) of these variables are restored.  The parameters are really auto
       variables that are initialized to a value provided in the function call.  Auto variables are different  than
       traditional local variables because if function A calls function B, B may access function A's auto variables
       by just using the same name, unless function B has called them auto variables.  Due to the  fact  that  auto
       variables and parameters are pushed onto a stack, bc supports recursive functions.

       The  function  body  is a list of bc statements.  Again, statements are separated by semicolons or newlines.
       Return statements cause the termination of a function and the return of a value.  There are two versions  of
       the  return statement.  The first form, "return", returns the value 0 to the calling expression.  The second
       form, "return ( expression )", computes the value of the expression and returns that value  to  the  calling
       expression.   There is an implied "return (0)" at the end of every function.  This allows a function to ter‐
       minate and return 0 without an explicit return statement.

       Functions also change the usage of the variable ibase.  All constants in the function body will be converted
       using the value of ibase at the time of the function call.  Changes of ibase will be ignored during the exe‐
       cution of the function except for the standard function read, which will always use  the  current  value  of
       ibase for conversion of numbers.

       Several  extensions have been added to functions.  First, the format of the definition has been slightly re‐
       laxed.  The standard requires the opening brace be on the same line as the  define  keyword  and  all  other
       parts must be on following lines.  This version of bc will allow any number of newlines before and after the
       opening brace of the function.  For example, the following definitions are legal.
              define d (n) { return (2*n); }
              define d (n)
                { return (2*n); }

       Functions may be defined as void.  A void function returns no value and thus may not be used  in  any  place
       that  needs  a  value.   A void function does not produce any output when called by itself on an input line.
       The key word void is placed between the key word define and the function name.  For  example,  consider  the
       following session.
              define py (y) { print "--->", y, "<---", "\n"; }
              define void px (x) { print "--->", x, "<---", "\n"; }
              py(1)
              --->1<---
              0
              px(1)
              --->1<---
       Since  py  is not a void function, the call of py(1) prints the desired output and then prints a second line
       that is the value of the function.  Since the value of a function that  is  not  given  an  explicit  return
       statement  is zero, the zero is printed.  For px(1), no zero is printed because the function is a void func‐
       tion.

       Also, call by variable for arrays was added.  To declare a call by variable array, the  declaration  of  the
       array  parameter in the function definition looks like "*name[]".  The call to the function remains the same
       as call by value arrays.

   MATH LIBRARY
       If bc is invoked with the -l option, a math library is preloaded and the default scale is set to  20.    The
       math  functions  will  calculate their results to the scale set at the time of their call.  The math library
       defines the following functions:

       s (x)  The sine of x, x is in radians.

       c (x)  The cosine of x, x is in radians.

       a (x)  The arctangent of x, arctangent returns radians.

       l (x)  The natural logarithm of x.

       e (x)  The exponential function of raising e to the value x.

       j (n,x)
              The Bessel function of integer order n of x.

   EXAMPLES
       In /bin/sh, the following will assign the value of "pi" to the shell variable pi.
               pi=$(echo "scale=10; 4*a(1)" | bc -l)

       The following is the definition of the exponential function used in the  math  library.   This  function  is
       written in POSIX bc.
              scale = 20

              /* Uses the fact that e^x = (e^(x/2))^2
                 When x is small enough, we use the series:
                   e^x = 1 + x + x^2/2! + x^3/3! + ...
              */

              define e(x) {
                auto  a, d, e, f, i, m, v, z

                /* Check the sign of x. */
                if (x<0) {
                  m = 1
                  x = -x
                }

                /* Precondition x. */
                z = scale;
                scale = 4 + z + .44*x;
                while (x > 1) {
                  f += 1;
                  x /= 2;
                }

                /* Initialize the variables. */
                v = 1+x
                a = x
                d = 1

                for (i=2; 1; i++) {
                  e = (a *= x) / (d *= i)
                  if (e == 0) {
                    if (f>0) while (f--)  v = v*v;
                    scale = z
                    if (m) return (1/v);
                    return (v/1);
                  }
                  v += e
                }
              }

       The  following  is  code that uses the extended features of bc to implement a simple program for calculating
       checkbook balances.  This program is best kept in a file so that it can be used many times without having to
       retype it at every use.
              scale=2
              print "\nCheck book program!\n"
              print "  Remember, deposits are negative transactions.\n"
              print "  Exit by a 0 transaction.\n\n"

              print "Initial balance? "; bal = read()
              bal /= 1
              print "\n"
              while (1) {
                "current balance = "; bal
                "transaction? "; trans = read()
                if (trans == 0) break;
                bal -= trans
                bal /= 1
              }
              quit

       The following is the definition of the recursive factorial function.
              define f (x) {
                if (x <= 1) return (1);
                return (f(x-1) * x);
              }

   READLINE AND LIBEDIT OPTIONS
       GNU  bc  can  be  compiled  (via a configure option) to use the GNU readline input editor library or the BSD
       libedit library.  This allows the user to do editing of lines before sending them to bc.  It also allows for
       a  history  of  previous lines typed.  When this option is selected, bc has one more special variable.  This
       special variable, history is the number of lines of history retained.  For readline, a  value  of  -1  means
       that  an  unlimited number of history lines are retained.  Setting the value of history to a positive number
       restricts the number of history lines to the number given.  The value of 0  disables  the  history  feature.
       The default value is 100.  For more information, read the user manuals for the GNU readline, history and BSD
       libedit libraries.  One can not enable both readline and libedit at the same time.

   DIFFERENCES
       This version of bc was implemented from the POSIX P1003.2/D11 draft and contains several differences and ex‐
       tensions  relative  to  the draft and traditional implementations.  It is not implemented in the traditional
       way using dc(1).  This version is a single process which parses and runs a byte code translation of the pro‐
       gram.   There  is an "undocumented" option (-c) that causes the program to output the byte code to the stan‐
       dard output instead of running it.  It was mainly used for debugging the parser and preparing the  math  li‐
       brary.

       A major source of differences is extensions, where a feature is extended to add more functionality and addi‐
       tions, where new features are added.  The following is the list of differences and extensions.

       LANG environment
              This version does not conform to the POSIX standard in the processing of the LANG  environment  vari‐
              able and all environment variables starting with LC_.

       names  Traditional  and  POSIX  bc  have single letter names for functions, variables and arrays.  They have
              been extended to be multi-character names that start with a letter and may contain  letters,  numbers
              and the underscore character.

       Strings
              Strings  are  not  allowed  to contain NUL characters.  POSIX says all characters must be included in
              strings.

       last   POSIX bc does not have a last variable.  Some implementations of bc use the period (.) in  a  similar
              way.

       comparisons
              POSIX  bc allows comparisons only in the if statement, the while statement, and the second expression
              of the for statement.  Also, only one relational operation is allowed in each of those statements.

       if statement, else clause
              POSIX bc does not have an else clause.

       for statement
              POSIX bc requires all expressions to be present in the for statement.

       &&, ||, !
              POSIX bc does not have the logical operators.

       read function
              POSIX bc does not have a read function.

       print statement
              POSIX bc does not have a print statement.

       continue statement
              POSIX bc does not have a continue statement.

       return statement
              POSIX bc requires parentheses around the return expression.

       array parameters
              POSIX bc does not (currently) support array parameters in full.  The POSIX grammar allows for  arrays
              in  function  definitions,  but does not provide a method to specify an array as an actual parameter.
              (This is most likely an oversight in the grammar.)  Traditional implementations of bc have only  call
              by value array parameters.

       function format
              POSIX bc requires the opening brace on the same line as the define key word and the auto statement on
              the next line.

       =+, =-, =*, =/, =%, =^
              POSIX bc does not require these "old style" assignment operators to be defined.  This version may al‐
              low these "old style" assignments.  Use the limits statement to see if the installed version supports
              them.  If it does support the "old style" assignment operators, the statement "a =- 1" will decrement
              a by 1 instead of setting a to the value -1.

       spaces in numbers
              Other  implementations of bc allow spaces in numbers.  For example, "x=1 3" would assign the value 13
              to the variable x.  The same statement would cause a syntax error in this version of bc.

       errors and execution
              This implementation varies from other implementations in terms of what code  will  be  executed  when
              syntax  and  other errors are found in the program.  If a syntax error is found in a function defini‐
              tion, error recovery tries to find the beginning of a statement and continue to parse  the  function.
              Once  a  syntax  error  is found in the function, the function will not be callable and becomes unde‐
              fined.  Syntax errors in the interactive execution code will invalidate the current execution  block.
              The  execution block is terminated by an end of line that appears after a complete sequence of state‐
              ments.  For example,
              a = 1
              b = 2
       has two execution blocks and
              { a = 1
                b = 2 }
       has one execution block.  Any runtime error will terminate the execution of the current execution block.   A
       runtime warning will not terminate the current execution block.

       Interrupts
              During  an  interactive session, the SIGINT signal (usually generated by the control-C character from
              the terminal) will cause execution of the current execution block to be interrupted.  It will display
              a  "runtime" error indicating which function was interrupted.  After all runtime structures have been
              cleaned up, a message will be printed to notify the user that bc is ready for more input.  All previ‐
              ously  defined  functions remain defined and the value of all non-auto variables are the value at the
              point of interruption.  All auto variables and function parameters are removed during  the  clean  up
              process.  During a non-interactive session, the SIGINT signal will terminate the entire run of bc.

   LIMITS
       The  following  are the limits currently in place for this bc processor.  Some of them may have been changed
       by an installation.  Use the limits statement to see the actual values.

       BC_BASE_MAX
              The maximum output base is currently set at 999.  The maximum input base is 16.

       BC_DIM_MAX
              This is currently an arbitrary limit of 65535 as distributed.  Your installation may be different.

       BC_SCALE_MAX
              The number of digits after the decimal point is limited to INT_MAX digits.  Also, the number of  dig‐
              its before the decimal point is limited to INT_MAX digits.

       BC_STRING_MAX
              The limit on the number of characters in a string is INT_MAX characters.

       exponent
              The value of the exponent in the raise operation (^) is limited to LONG_MAX.

       variable names
              The  current  limit  on  the number of unique names is 32767 for each of simple variables, arrays and
              functions.

ENVIRONMENT VARIABLES
       The following environment variables are processed by bc:

       POSIXLY_CORRECT
              This is the same as the -s option.

       BC_ENV_ARGS
              This is another mechanism to get arguments to bc.  The format is the same as the command  line  argu‐
              ments.   These  arguments  are  processed first, so any files listed in the environment arguments are
              processed before any command line argument files.  This allows the user to set up "standard"  options
              and  files  to  be processed at every invocation of bc.  The files in the environment variables would
              typically contain function definitions for functions the user wants defined every time bc is run.

       BC_LINE_LENGTH
              This should be an integer specifying the number of characters in an output line  for  numbers.   This
              includes  the  backslash and newline characters for long numbers.  As an extension, the value of zero
              disables the multi-line feature.  Any other value of this variable that is less than 3 sets the  line
              length to 70.

DIAGNOSTICS
       If  any  file  on the command line can not be opened, bc will report that the file is unavailable and termi‐
       nate.  Also, there are compile and run time diagnostics that should be self-explanatory.

BUGS
       Error recovery is not very good yet.

       Email bug reports to bug-bc@gnu.org.  Be sure to include the  word  ``bc''  somewhere  in  the  ``Subject:''
       field.

AUTHOR
       Philip A. Nelson
       philnelson@acm.org

ACKNOWLEDGEMENTS
       The  author  would like to thank Steve Sommars (Steve.Sommars@att.com) for his extensive help in testing the
       implementation.  Many great suggestions were given.  This is a much better product due to his involvement.

GNU Project                                          2006-06-11                                               bc(1)